D-Optimality-Guided Reinforcement Learning for Efficient Open-Loop Calibration of a 3-DOF Ankle Rehabilitation Robot

TL;DR

This paper introduces a D-optimality-guided reinforcement learning approach to efficiently calibrate a 3-DOF ankle rehabilitation robot, significantly reducing calibration effort while ensuring accurate alignment.

Contribution

It develops a novel two-stage calibration framework combining linear parameter identification with a PPO-based posture selection guided by D-optimality, improving calibration efficiency and robustness.

Findings

PPO policy selects more informative postures than random methods.

Calibration with four D-optimal postures yields better parameter estimates.

The approach reduces calibration time while maintaining high accuracy.

Abstract

Accurate alignment of multi-degree-of-freedom rehabilitation robots is essential for safe and effective patient training. This paper proposes a two-stage calibration framework for a self-designed three-degree-of-freedom (3-DOF) ankle rehabilitation robot. First, a Kronecker-product-based open-loop calibration method is developed to cast the input-output alignment into a linear parameter identification problem, which in turn defines the associated experimental design objective through the resulting information matrix. Building on this formulation, calibration posture selection is posed as a combinatorial design-of-experiments problem guided by a D-optimality criterion, i.e., selecting a small subset of postures that maximises the determinant of the information matrix. To enable practical selection under constraints, a Proximal Policy Optimization (PPO) agent is trained in simulation to choose 4 informative postures from a candidate set of 50. Across simulation and real-robot evaluations, the learned policy consistently yields substantially more informative posture combinations than random selection: the mean determinant of the information matrix achieved by PPO is reported to be more than two orders of magnitude higher with reduced variance. In addition, real-world results indicate that a parameter vector identified from only four D-optimality-guided postures provides stronger cross-episode prediction consistency than estimates obtained from a larger but unstructured set of 50 postures. The proposed framework therefore improves calibration efficiency while maintaining robust parameter estimation, offering practical guidance for high-precision alignment of multi-DOF rehabilitation robots.